Exploratory Numerical Assessment of Hybrid-Melting-Point Phase Change Materials for Building Envelopes

Abstract

Phase change materials (PCMs) have been widely investigated for latent thermal energy storage in building envelopes; however, conventional single-melting-point PCMs often exhibit limited adaptability under dynamically varying thermal conditions. This study investigates the thermodynamic feasibility of hybrid-melting-point PCMs to improve transient thermal regulation in multilayer building wall systems. A transient numerical model was developed to evaluate wall assemblies incorporating single and hybrid PCM configurations under structured dynamic thermal loading conditions representing mild, hot, and cold regimes. To isolate the influence of melting-point distribution, hybrid systems containing multiple phase-transition temperatures were compared against conventional single-transition PCM systems with identical total latent heat capacities. The results demonstrate that distributing melting thresholds broadens the effective activation temperature range and enhances attenuation of indoor temperature fluctuations under varying thermal loads. Compared with the conventional single-melting-point system, the proposed hybrid configuration reduced peak indoor temperature by up to 18.5% and increased the minimum indoor temperature by up to 51.9%. Additional material-level simulations revealed that staged phase transitions promote sequential latent heat activation and prolong thermal buffering behavior. The findings suggest that hybrid-melting-point PCMs can improve the transient thermal adaptability of PCM-integrated building envelopes without increasing total latent heat storage capacity. The present study is intended as an exploratory thermodynamic feasibility assessment rather than a climate-specific annual building-energy prediction framework.

1. Introduction

The building sector is responsible for approximately 40% of the total U.S. energy consumption, which is greater than that consumed by either industry (32%) or transportation (29%), according to the U.S. DOE report 2019 [1,2,3]. Energy consumed in buildings is expected to further increase by 65% between 2018 and 2050 [3]. Among different energy end uses, space heating and cooling account for more than half (51% in 2015) of U.S. households’ annual energy consumption [1,2,3]. As a comparison, indoor space heating accounts for 70% of the energy demand of European households [4]. Improving energy efficiency in buildings has therefore become a central strategy for reducing energy consumption and advancing sustainability goals worldwide. Introducing a passive heating/cooling strategy by means of a thermal energy storage (TES) system into building thermal management shows high potential to reduce electrical energy depleted by the heating, ventilation, and air conditioning (HVAC) system, and thus becomes a primary backbone of enhancing building energy efficiency [5,6]. The TES system is a temporary energy storage medium that can be used to store the renewable energy generated from solar radiation or nighttime cold for later use. Among various approaches, latent heat storage using PCMs is particularly promising due to their high energy storage density and ability to moderate indoor temperature fluctuations within a narrow temperature range. During the last few decades, a large number of researchers have focused on the integration of this system in buildings for energy saving [7,8,9,10,11,12,13,14]. It turns out to be a promising technology to reduce the energy consumption in buildings [15], to increase building energy efficiency [16], to shift the electrical energy peak load [13,17], and to maintain indoor thermal comfort for a longer time [18]. TES can be implemented by sensible heat, chemical heat, and latent heat. When used for thermal management of buildings, latent heat storage based on PCMs is gaining increasing interest due to its advantages, such as high energy storage capacity, isothermal nature during the phase change process, and high potential to increase the thermal inertia of the building envelope. In recent years, both experimental and numerical investigations on the utilization of PCMs in buildings have been carried out to explore the criteria of PCM selection for building applications, the development of high-performance PCMs, methods of incorporation into building envelopes, crucial design parameters influencing building energy efficiency, and the thermal performance of PCM-based buildings subjected to various loading conditions.

The effectiveness of PCM-based envelopes is highly dependent on the melting temperature of the material [9,19,20,21,22,23,24,25]. Despite numerous investigations on PCMs in different applications, only a few have addressed the relationship between the overall usage tendency of PCMs and the corresponding building thermal performance. Most prior research has focused on identifying an optimal single melting point for a given climate or season [6,9]. While such designs can achieve seasonal benefits, they lack adaptability under dynamic outdoor conditions, limiting their performance across varying thermal loads. Emerging work on composite or tunable PCMs suggests that broader or multiple melting ranges may improve year-round utilization of latent heat, but systematic studies and practical implementations remain limited.

Although cascaded and hybrid PCM systems have been explored in previous studies [26,27,28,29,30], most existing investigations primarily focus on climate-specific optimization, generalized energy-saving evaluation, or material-level thermal storage enhancement. Limited studies have systematically investigated the transient thermodynamic influence of staged melting-point distributions under controlled dynamic loading conditions while maintaining identical total latent heat storage capacity across PCM configurations. Furthermore, the mechanistic evolution of sequential phase-transition activation behavior within hybrid PCM systems remains insufficiently clarified.

Accordingly, the present study investigates the following research questions:

(1)

How does distributing PCM melting thresholds influence transient thermal regulation behavior under dynamically varying thermal conditions?

(2)

Can hybrid-melting-point PCM systems improve overheating mitigation and cold-regime thermal retention relative to conventional single-transition PCM systems while maintaining identical latent heat capacity?

(3)

How does staged phase-transition evolution influence transient thermal buffering behavior within hybrid PCM systems?

Based on these questions, the central hypothesis of this study is that distributing phase-transition temperatures across multiple thermal intervals can broaden latent heat activation ranges and improve transient thermal adaptability without increasing total latent heat storage capacity.

The primary contribution of this study is its examination of the influence of distributed melting thresholds on transient thermal regulation under dynamically varying thermal conditions, while maintaining an identical total latent heat capacity. The study further provides material-level thermodynamic interpretation of staged latent heat activation through isolated PCM block simulations, offering mechanistic insight into the operational adaptability of hybrid-melting-point PCM systems.

2. Research Motivation and Problem Formulation

2.1. Performance Constraints of Single-Melting-Point PCM Systems

PCMs have been widely integrated into building envelopes to reduce indoor temperature fluctuations, delay peak thermal loads, and improve thermal comfort. Among various applications, wall-integrated PCM systems dominate reported building-envelope implementations (accounting for 72.4% of applications, as shown in Figure 1), due to their large exposure area and direct interaction with outdoor thermal loading [21]. Historically, the selection of a PCM is dictated by its melting point. Figure 2 shows the general distribution tendency of the melting temperature of the PCMs in building applications. The melting temperature of the selected PCMs ranges from 16 °C to 40 °C, covering a large temperature span up to 24 °C. The big center of the Gaussian distribution curve fitted from the frequency distribution or different melting temperatures is 26.5 °C. This clustering occurs because designers primarily aim to align the phase transition with the human thermal comfort zone (around 24 °C) [22,23].

However, PCM is only effective if its charging and discharging processes are fully activated by the diurnal temperature swing. Alawadhi [24] demonstrated this by comparing PCMs with melting points of 27 °C, 37 °C, and 47 °C; only the material near the middle of the specific operating temperature range effectively reduced heat flux, while the others remained trapped in either a purely liquid or purely solid state.

This creates a critical vulnerability: buildings experience pronounced diurnal and seasonal weather variability. A PCM optimized for a specific season often becomes dormant when the weather changes. Saffari et al. [25] found that for a building in Madrid, a 27 °C PCM maximized summer cooling savings, whereas a 23 °C PCM was required for winter heating effectiveness. Similarly, Li et al. [9,10] demonstrated that, in climates with pronounced seasonal variation, such as Austin and Minneapolis, the optimal melting point varies substantially between 18 °C and 30 °C by month. Consequently, integrating a standard single-melting-point PCM inherently leads to the underutilization of latent storage for significant portions of the year, preventing buildings from achieving maximum annual energy savings.

2.2. Evolution Toward Hybrid Systems and Current Gaps

To resolve this seasonal mismatch, the U.S. Department of Energy and various materials scientists have proposed the development of solid-state PCMs and composite mixtures with tunable thermal energy storage [26,27,28]. These material-level advances introduce the possibility of “smart” building envelopes capable of staging energy release across wider temperature intervals.

Despite these material innovations, the systematic, building-scale evaluation of hybrid or multi-melting-point strategies remains highly limited. The existing literature is heavily saturated with studies optimizing single-point PCMs for specific climate zones [29,30], but there is a distinct lack of transient numerical studies directly comparing hybrid-melting-point configurations against conventional single-transition systems under identical, dynamic seasonal loading. Furthermore, the intrinsic heat-transfer mechanisms, specifically how multi-stage phase fronts propagate and interact within a singular building envelope, have not been fully elucidated.

These knowledge gaps form the primary motivation for this study. To advance the design of resilient building envelopes beyond single-point optimization, it is necessary to mathematically quantify the adaptability of staged phase transitions. Building upon this motivation, Section 3 details the governing equations and dynamic loading protocols used to evaluate the proposed hybrid-melting-point wall assembly.

3. Modeling of PCM-Reinforced Building Envelopes

3.1. Wall Configurations and PCM Design with Hybrid Melting Points

To investigate the thermodynamic influence of staged latent heat storage on building-envelope thermal regulation, a representative light-frame residential wall assembly commonly used in North American construction was adopted as the computational domain. The use of a standardized wall assembly enables consistent comparison with previous PCM-integrated envelope studies while maintaining practical relevance for residential applications. Three wall configurations were defined to isolate and quantify the thermal contribution of phase change materials under identical geometric and boundary conditions.

As shown in Figure 3, Reference Wall 1 (RW1) serves as the baseline configuration. It consists, from interior to exterior, of a 12.7 mm gypsum wallboard, a 30 mm insulation layer, and a 20.5 mm oriented strand board (OSB) sheathing. The insulation thickness was intentionally reduced relative to conventional practice to enhance thermal coupling between indoor and outdoor environments and amplify the measurable impact of PCM integration. This controlled simplification facilitates clearer interpretation of latent heat effects without altering comparative validity among configurations.

Reference Wall 2 (RW2) introduces a conventional single-melting-point PCM layer of 10 mm thickness between the gypsum board and the insulation layer (see Figure 3). The PCM melting temperature is fixed at 24 °C, corresponding to the central value of typical indoor thermal comfort ranges reported in the literature. This configuration represents the prevalent design paradigm in which PCM selection targets a single optimized transition temperature for seasonal energy savings.

As illustrated in Figure 4, the hybrid wall configuration retains the geometric characteristics of RW2 but replaces the single-transition PCM with a composite matrix comprising three equal-volume fractions exhibiting melting temperatures of 16 °C, 24 °C, and 32 °C. The total PCM thickness and aggregate latent heat capacity are maintained equivalent to RW2 to ensure that performance differences arise from transition staging rather than increased storage capacity.

The selected melting thresholds represent cold-condition activation (16 °C), thermal comfort-zone regulation (24 °C), and elevated-temperature buffering (32 °C). The staged configuration is intended to broaden the operational temperature range over which latent heat storage can be effectively activated under varying thermal conditions. Unlike conventional PCM studies focused on identifying a single optimized melting point for a specific climate or season, the present configuration enables systematic evaluation of how distributed phase-transition temperatures influence transient thermal regulation while maintaining identical latent heat capacity across wall assemblies. The present study focuses on thermodynamic feasibility and staged latent heat activation behavior rather than manufacturing implementation. Practical considerations associated with PCM encapsulation, multilayer integration, long-term material compatibility, and prevention of cross-contamination between PCM layers remain important topics requiring future experimental investigation.

3.2. Methodology for Modeling Building Envelopes with PCM Layer

3.2.1. Governing Equations and PCM Formulation

A two-dimensional (2D) transient heat-conduction model was developed in COMSOL Multiphysics^®version 5.5 to simulate the thermal response of multilayer wall assemblies incorporating PCM layers. Although heat transfer through the wall thickness is dominant and effectively one-dimensional under the imposed boundary conditions, a 2D formulation was retained to provide numerical flexibility for multilayer PCM configurations and to better capture localized phase-transition evolution within PCM domains. In the present coordinate system, the $x$-direction represents the through-thickness heat-transfer direction across the wall assembly from the exterior surface toward the interior gypsum layer, while the $y$-direction denotes the in-plane direction retained within the 2D computational framework.

Heat transfer within both solid and liquid PCM phases was assumed to be conduction-dominated. Natural convection within the liquid PCM phase was neglected because the PCM layers are geometrically confined by adjacent gypsum and insulation layers, substantially restricting fluid motion during melting. The model relies on several fundamental assumptions: (a) all material layers are homogeneous and isotropic; (b) heat transfer through the wall assembly is effectively one-dimensional (1D); (c) thermal expansion is negligible; (d) thermophysical properties remain constant, with the exception of the PCM density across phase states; and (e) contact resistance between adjacent structural layers is negligible.

The transient thermal behavior is governed by the standard partial differential equation [31]:

$${\displaystyle \frac{\partial }{\partial x}}\left(\lambda {\displaystyle \frac{\partial T}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(\lambda {\displaystyle \frac{\partial T}{\partial y}}\right)=\rho C_P{\displaystyle \frac{\partial T}{\partial t}},$$

(1)

where $T$ is the temperature (K), $\lambda$ is the thermal conductivity of the material (W/m K), $\rho$ is the density of the material (kg/m³), and $C_P$ is the specific heat of the material (J/kg K). Under the assumption of dominant through-thickness heat transfer, Equation (1) reduces to the one-dimensional transient conduction form [31]:

$${\displaystyle \frac{{\partial }^{2}T}{{\partial x}^2}}={\displaystyle \frac{\rho C_P}{\lambda }}{\displaystyle \frac{\partial T}{\partial t}},$$

(2)

Figure 5 schematically illustrates the thermodynamic interpretation of PCM phase-transition behavior employed in the present study. Figure 5a presents the classical idealized phase transition occurring instantaneously at a theoretical melting temperature $T_m$, where latent heat appears as an abrupt enthalpy discontinuity. However, practical PCMs typically exhibit phase transitions over a finite temperature interval due to material heterogeneity and non-equilibrium melting behavior. Therefore, as illustrated in Figure 5b, the PCM phase transition was modeled over a finite interval bounded by the solidus temperature $T_s$ and liquidus temperature $T_l$, enabling gradual latent heat absorption and release during melting.

The phase-transition process was modeled using the apparent heat-capacity (AHC) method, in which latent heat effects are distributed continuously over the phase-transition interval rather than applied as an instantaneous enthalpy jump. In this framework, the total PCM enthalpy (Figure 5b) consists of sensible heat and phase-transition enthalpy contributions [32,33]:

$$H(T)=\int c_p(T)dT+∆h_t\xi (T),$$

(3)

where $∆h_t \mathrm{o}\mathrm{r} L$ is the latent heat of fusion (J/kg) and $\xi \left(T\right)$ is the temperature-dependent liquid mass fraction function varying continuously from 0 (fully solid) to 1 (fully liquid) over the transition interval. The liquid mass fraction function is defined as:

$$\xi (T)={\displaystyle \frac{m^l}{m^l+m^s}},$$

(4)

where $m^s$ and $m^l$ are the masses of solid and liquid phase, respectively, and $0\le \xi \left(T\right)\le 1.$ Accordingly, the effective apparent heat capacity, $C_p^{eff}\left(T\right),$ can be expressed as (Figure 5c) [32]:

$$C_p^{eff}(T)=\xi (T)C_p^l+(1-\xi (T))C_p^s+L{\displaystyle \frac{d\xi \left(T\right)}{dT}},$$

(5)

where $C_p^s$ and $C_p^l$ denote the sensible heat capacities of the solid and liquid PCM phases, respectively. The derivative term $L\ast \left({\displaystyle \frac{d\xi }{dT}}\right)$ represents the distributed latent heat contribution during phase transition.

As illustrated schematically in Figure 5c, the latent heat contribution appears as a peak in the apparent heat-capacity curve, while the integrated area between the apparent heat-capacity curve and the sensible heat baseline corresponds to the total latent heat of fusion $L$.

The effective PCM density and thermal conductivity were expressed as:

$${\rho }_{PCM}={\rho }^s (1-\xi (T\left)\right)+{\rho }^l \xi \left(T\right),$$

(6)

$${\lambda }_{PCM}={\lambda }^s(1-\xi (T\left)\right)+{\lambda }^l\xi \left(T\right),$$

(7)

where superscripts $s$ and $l$ denote solid and liquid phases, respectively.

In the present exploratory thermodynamic analysis, identical thermal conductivity values were assumed for the solid and liquid PCM phases due to limited phase-dependent conductivity data availability and to isolate the influence of melting-point distribution on transient thermal regulation behavior. Although practical PCM systems may exhibit phase-dependent conductivity variation, the present simplification enables controlled comparative evaluation among PCM configurations under identical thermophysical assumptions.

The previously described apparent heat-capacity formulation was implemented in COMSOL Multiphysics^® [34], to simulate transient PCM phase-transition behavior within the multilayer wall assemblies. The baseline thermophysical properties assigned to the standard building materials are as follows: gypsum board ($\rho$ = 800 kg/m³, CP = 1.09 kJ/kg·K, λ = 0.16 W/m·K); insulating layer ($\rho$ = 12.7 kg/m³, CP = 0.84 kJ/kg·K, λ = 0.045 W/m·K); OSB ($\rho$ = 650 kg/m³, CP = 1.21 kJ/kg·K, λ = 0.13 W/m·K) and PCM ($\rho$ = 880 (solid)/760 (liquid) kg/m³, CP = 2.0 kJ/kg·K, λ = 0.2 W/m·K). To represent realistic PCM melting behavior, the phase-transition interval was prescribed as 5 °C rather than assuming an idealized instantaneous transition at a single melting temperature [35].

3.2.2. Boundary Conditions and Controlled Thermal Loading

The boundary conditions of the governing equation are

$$T \left(0,t\right)=T_i (x=0)$$

(8a)

$$T \left(\delta ,t\right)=T_e (x=\delta )$$

(8b)

where $T_i$ and $T_e$ denote the interior and exterior surface temperatures, respectively, and $\delta$ represents total wall thickness.

The initial condition needed to solve the system of equations is a constant temperature for the whole wall that is equal to the interior temperature (24 °C). Figure 6 presents the imposed exterior solar-air temperature profile used in the simulations. The loading sequence consists of four consecutive 7-day thermal fragments representing mild, hot, mild, and cold operating conditions. In a typical cold season, the temperature applied to the wall exterior surface is assumed to swing between 4 °C and 24 °C, centered at 14 °C. On a typical mild season, the temperature is assumed to swing between 14 °C and 34 °C, centered at 24 °C. In contrast, in a typical hot season, the temperature is higher, which is assumed to swing between 24 °C and 44 °C, centered at 34 °C. The overall temperature profile of the input loading condition consisted of four 7-day temperature fragments following the order mild–hot–mild–cold to simulate a seasonal temperature change.

Under this loading condition, the instantaneous temperature at the interior gypsum-board surface was recorded to evaluate transient thermal regulation performance. For isolated PCM block simulations, the initial PCM temperature was set to 18 °C while a constant exterior temperature of 35 °C was imposed to investigate staged phase-transition behavior independent of wall-layer interactions. The simplified sinusoidal thermal loading was intentionally employed to isolate the intrinsic thermodynamic response of staged phase-transition systems under controlled dynamic conditions. The objective of the present study is not climate-specific annual energy prediction, but rather a mechanistic evaluation of transient latent heat activation behavior across varying thermal regimes.

Although real climatic conditions exhibit substantially greater variability than idealized sinusoidal loading, the controlled loading framework enables systematic comparison among PCM configurations while minimizing confounding environmental effects. It should be noted that the present loading conditions are intended for controlled thermodynamic interpretation and do not represent full annual climatic variability, HVAC operation, or location-specific weather conditions.

3.2.3. Mesh Sensitivity and Model Calibration

A mesh sensitivity analysis was conducted to ensure numerical stability, solution convergence, and computational efficiency of the transient heat-transfer simulations. Temperature responses predicted at 24 h, 48 h, and 96 h were compared using five mesh densities, namely coarse, normal, fine, extra fine, and extremely fine meshes. The comparison results are presented in Figure 7. As shown in Figure 7, noticeable variations in predicted temperatures are observed between the coarse and normal mesh configurations, indicating insufficient spatial resolution for accurately capturing transient thermal gradients and phase-transition behavior. However, the differences among the fine, extra fine, and extremely fine meshes become progressively smaller, demonstrating convergence of the numerical solution with increasing mesh refinement. To further clarify the numerical discretization details, the corresponding element numbers and relative computational time requirements associated with each mesh density were additionally incorporated into Figure 7. The coarse, normal, fine, extra fine, and extremely fine meshes consisted of approximately 785, 884, 925, 3110, and 10,885 elements, respectively. Meanwhile, the corresponding relative computational times increased progressively from 15 min for the coarse mesh to 44 min for the extremely fine mesh. These additional mesh statistics were incorporated to provide a more transparent comparison between numerical accuracy and computational expense associated with mesh refinement.

The extra fine mesh produced temperature predictions within approximately 0.2% of those obtained using extremely fine mesh while reducing computational time by approximately 31.8%. Considering both numerical accuracy and computational efficiency, the extra fine mesh configuration was selected for all subsequent simulations. The present mesh sensitivity analysis confirms that the predicted transient thermal responses are not significantly influenced by further mesh refinement beyond the selected mesh density. This verification improves confidence in the numerical stability and consistency of the reported thermal regulation results.

The numerical formulation adopted in this study follows previously reported PCM heat-transfer modeling approaches developed in the authors’ earlier investigations (Li et al., 2021a,b [9,10]), where comparable transient thermal behaviors were observed. It should be noted that the present study is intended as an exploratory thermodynamic feasibility assessment rather than a fully validated building-energy prediction framework. The focus is therefore placed on controlled comparative evaluation of staged phase-transition behavior under identical loading conditions.

3.2.4. Performance Indexes

The thermal performance of the investigated wall assemblies was evaluated using the decrement factor, increment factor, and intensity of thermal discomfort (ITD) indices [9,10,36]. The decrement factor represents the percentage reduction in peak indoor temperature relative to the reference wall without PCM integration, while the increment factor quantifies the percentage increase in minimum indoor temperature relative to the reference configuration. Together, these metrics evaluate the ability of PCM-integrated walls to attenuate overheating and mitigate excessive cooling.

To further evaluate thermal comfort performance, overheating and overcooling intensity indices were adopted following previous studies. The thermal comfort range was defined between 22 °C and 28 °C. Figure 8 separately illustrates the definitions of overheating and overcooling used in the ITD calculation. In Figure 8a, overheating is evaluated when the indoor operative temperature exceeds the upper comfort limit of 28 °C. The shaded region above 28 °C is defined as the overheating discomfort area, $A_1$, while the shaded region within the comfort band between 22 °C and 28 °C is defined as the corresponding comfort-retention area, $A_2$. Therefore, a larger $A_2$ and smaller $A_1$ indicate better overheating control. In Figure 8b, overcooling is evaluated when the indoor operative temperature falls below the lower comfort limit of 22 °C. The shaded region below 22 °C is defined as the overcooling discomfort area, $B_1$, while the shaded region within the comfort band is defined as the corresponding comfort-retention area, $B_2$. Therefore, a larger $B_2$ and smaller $B_1$ indicate improved thermal retention under cold conditions.

Based on these area definitions, the overheating and overcooling ITD indices are reformulated as normalized comfort-retention ratios:

$$IT{D}_{up}={\displaystyle \frac{{\int }_P(T_{op}-T_{upper})\mathrm{d}\mathrm{t}}{{\int }_P{T}_{op}\mathrm{d}\mathrm{t}}}={\displaystyle \frac{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t} \mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}}{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t} \mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}+\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}}}={\displaystyle \frac{\mathrm{A}2}{\mathrm{A}1+\mathrm{A}2}}\ast 100\%$$

(9)

$$IT{D}_{down}={\displaystyle \frac{{\int }_P(T_{op}-T_{lower})\mathrm{d}\mathrm{t}}{{\int }_P{T}_{op}\mathrm{d}\mathrm{t}}}={\displaystyle \frac{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t} \mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}}{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t} \mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}+\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}}}={\displaystyle \frac{\mathrm{B}2}{\mathrm{B}1+\mathrm{B}2}}$$

(10)

where $A_1$ is the cumulative overheating discomfort area above 28 °C, $A_2$ is the corresponding comfort-retention area within the 22–28 °C comfort band, $B_1$ is the cumulative overcooling discomfort area below 22 °C, and $B_2$ is the corresponding comfort-retention area within the comfort band. $T_{op}$ denotes the indoor operative temperature, $T_{lower}$ and $T_{upper }$ represent the lower and upper thermal comfort limits, respectively, and $P$ denotes the evaluation period.

With the present formulation, an ITD value of 100% indicates that no temperature excursion beyond the corresponding thermal comfort threshold occurred during the evaluated thermal fragment. Specifically, $IT{D}_{up}=100\%$ indicates that the overheating discomfort area $A_1$ becomes zero, indicating that the indoor operative temperature remained entirely below the upper comfort limit of 28 °C throughout the evaluation period. Similarly, $IT{D}_{down}=100\%$ indicates that the overcooling discomfort area $B_1$ becomes zero, meaning the indoor operative temperature remained above the lower comfort limit of 22 °C during the corresponding fragment.

4. Results and Discussion

In this section, the transient thermal performance of the external building wall incorporating the hybrid-melting-point PCM is evaluated under controlled dynamic thermal loading conditions. The proposed hybrid wall is compared against the non-reinforced Reference Wall 1 (RW1) and the single-melting-point Reference Wall 2 (RW2). The imposed loading sequence consists of four 7-day thermal fragments representing mild, hot, mild, and cold regimes, respectively. The resulting instantaneous temperatures at the interior gypsum-board interface were extracted to investigate staged latent heat activation behavior and thermal regulation effectiveness under varying thermal conditions.

4.1. Transient Thermal Performance Under Mild Conditions (Fragments I and III)

Figure 9 presents the transient indoor temperature responses of RW1, RW2, and the proposed hybrid wall under the imposed dynamic loading conditions. Under these moderate thermal conditions, the thermal performance of RW2 exhibits a slight superiority over the proposed hybrid wall in restricting maximum temperature amplitude. This behavior can be attributed to the larger proportion of PCM material undergoing phase transition near 24 °C in RW2. Since the exterior loading conditions remain centered near the thermal comfort range during the mild fragments, the single-transition PCM layer remains highly active throughout the thermal cycle.

Although the hybrid configuration exhibits slightly reduced peak attenuation during these fragments, indoor temperatures remain largely confined within the thermal comfort range, demonstrating that staged melting-point distributions can maintain effective thermal regulation under moderate loading conditions.

4.2. Overheating Mitigation Under Hot Thermal Regimes (Fragment II)

Under hot dominant loading conditions (24 °C to 44 °C, centered at 34 °C), the thermal performance differences between the single-transition and hybrid PCM systems become more evident. As shown in the histogram of 7-day average extremes (Figure 10a), the maximum indoor temperature of the non-reinforced RW1 reaches 40.4 °C during the severe heating cycle.

The integration of the 10 mm single-point PCM (24 °C, 180 J/g) in RW2 reduces this peak to 37.8 °C, corresponding to a decrement factor of 6.4% relative to RW1. However, the thermal attenuation capability of RW2 becomes limited under sustained high-temperature exposure because the PCM layer rapidly completes its phase transition and subsequently behaves primarily as a sensible heat storage medium.

Compared with RW1 (reference wall without PCM integration), the proposed hybrid PCM wall reduced the maximum indoor temperature by approximately 18.5% during Fragment II, indicating enhanced attenuation of overheating under elevated thermal-loading conditions. This improved overheating mitigation can be attributed to staged latent heat activation within the PCM16, PCM24, and PCM32 components. Under elevated temperatures, the higher-transition PCM fraction remains partially active after lower-transition components have completed melting, thereby extending latent heat absorption over a broader temperature range. The results indicate that distributing phase-transition temperatures across multiple thermal ranges can improve overheating mitigation under dynamically varying thermal conditions without increasing total latent heat storage capacity.

4.3. Thermal Retention Under Cold Thermal Regimes (Fragment IV)

During the cold thermal fragment (Fragment IV), the influence of melting-point distribution on thermal retention becomes more apparent. As illustrated in Figure 10b, the minimum indoor temperature of RW1 drops to 7.9 °C. The inclusion of the single-transition PCM layer in RW2 increases the minimum to 10.6 °C, corresponding to an increment factor of 34.2% relative to RW1. However, because exterior temperatures frequently remain below its 24 °C phase-transition threshold, the latent heat storage potential of RW2 becomes only partially activated during the cooling cycle.

Conversely, relative to RW1 (reference wall without PCM integration), the hybrid wall further increases the minimum indoor temperature to 12.0 °C, by approximately 51.9% during Fragment IV, demonstrating improved thermal retention under cold thermal-loading conditions. This improved cold-regime thermal retention is associated with the staged solidification behavior of the hybrid PCM system. As higher-transition PCM fractions release latent heat during early cooling stages, the PCM16 fraction remains thermally active at lower temperatures, thereby prolonging thermal buffering during continued cooling. These results suggest that hybrid-melting-point PCM systems can extend the effective operational range of latent heat storage under both elevated and reduced thermal loading conditions.

4.4. Thermal Comfort Evaluation Using ITD Metrics

To further quantify thermal comfort performance, the overheating and overcooling intensity indices defined in Section 3.2.4 were evaluated for all wall configurations. As illustrated schematically in Figure 8, the overheating and overcooling regions correspond to the cumulative temperature excursions above 28 °C and below 22 °C, respectively. Smaller shaded discomfort regions, therefore, indicate improved thermal regulation performance.

The calculated ITD values summarized in

Table 1. Normalized overheating ($IT{D}_{up}$) and overcooling ($IT{D}_{down}$) thermal comfort-retention indices for RW1, RW2, and the proposed hybrid PCM wall under different thermal fragments.

	ITDup (%)			ITDdown (%)
	RW1	RW2	Proposed Wall	RW1	RW2	Proposed Wall
Fragment I	86.5	100	100	79.9	100	98.9
Fragment II	65.7	74.7	85.2	100	100	100
Fragment III	85.2	96.9	94.5	78.6	100	100
Fragment IV	100	100	96.7	59.4	77.4	76.5
Total	84.4	92.9	94.1	79.5	92.7	93.9

indicate that the hybrid wall substantially improves thermal comfort retention relative to RW1 and RW2. Over the aggregate 28-day simulation, The ITD_up values improved from 84.4% (RW1) to 92.9% (RW2), peaking at 94.1% for the hybrid wall. Similarly, ITD_down improved from 79.5% (RW1) to 92.7% (RW2), reaching 93.9% for the hybrid configuration.

Close observation indicates that several entries in Table 1 reached ITD values of 100%, indicating that no overheating or overcooling discomfort occurred during the corresponding thermal fragments under the imposed loading conditions. For example, during Fragment II, all wall configurations exhibited $IT{D}_{down}=100\%$, since the indoor operative temperatures remained entirely above the lower comfort threshold of 22 °C throughout the hot thermal regime. Similarly, several configurations were achieved $IT{D}_{up}=100\%$ during mild or cold fragments where indoor temperatures did not exceed the upper comfort limit of 28 °C. These results suggest that, under specific thermal loading regimes, the PCM-integrated wall systems were capable of fully maintaining indoor temperatures within the prescribed thermal comfort bounds.

Fragment-specific analysis further reveals that the hybrid PCM configuration provides improved overheating mitigation during the hot thermal regime (Fragment II), and enhanced thermal retention during the cold regime (Fragment IV). During Fragment II, the hybrid wall achieved an ITDup value of 85.2%, compared with 74.7% for RW2 and 65.7% for RW1. Similarly, under Fragment IV, the hybrid configuration exhibited improved overcooling regulation relative to RW1 and comparable thermal comfort retention relative to RW2. The improved ITD performance is consistent with the staged latent heat activation behavior previously discussed in Section 4.2 and Section 4.3. By distributing phase-transition temperatures across multiple thermal ranges, the hybrid PCM system reduces cumulative overheating and overcooling duration under dynamically varying thermal conditions.

4.5. Influence of Latent Heat Capacity on Thermal Regulation

To evaluate the influence of latent heat storage magnitude independent of melting-point distribution, the proposed hybrid wall was further investigated using two different total latent heat capacities: 180 J/g and 360 J/g.

As plotted in the instantaneous temperature profiles (Figure 11), increasing latent heat capacity reduces indoor temperature fluctuations and prolongs thermal buffering duration. The hybrid wall containing PCM with 180 J/g latent heat exhibits indoor temperature oscillations between 10.5 °C and 36.7 °C, resulting in a maximum fluctuation span of 26.2 °C. Doubling the latent heat capacity to 360 J/g constrains this oscillation strictly between 11.0 °C and 31.7 °C, narrowing the fluctuation to 20.7 °C. This represents a 20.9% reduction in maximum temperature fluctuation.

Increasing latent heat capacity, therefore, improves transient thermal stability by extending the duration of latent heat absorption and release during cyclic thermal loading. The increased storage capacity extends the duration of indoor thermal comfort by 17.6% and induces an average temporal phase shift of approximately 3 h for both maximum and minimum peaks. This empirical evidence suggests that the higher-capacity PCM system introduces a measurable temporal delay in peak indoor temperature response, indicating enhanced thermal inertia of the wall assembly. The results further indicate that the thermal regulation performance of PCM-integrated wall systems depends not only on the magnitude of latent heat storage capacity, but also on the distribution of phase-transition temperatures across the operational thermal range.

To sum up, the results presented in this section demonstrate that hybrid-melting-point PCM systems can improve transient thermal adaptability by extending latent heat activation over broader temperature intervals. While the total latent heat capacity remains unchanged relative to the single-transition PCM configuration, staged melting behavior enables more continuous thermal buffering under varying thermal conditions.

5. Thermodynamics of Hybrid PCM Behavior

To further interpret the transient thermal responses observed in Section 4, isolated PCM computational domains were investigated independently from the multilayer wall system. This material-level analysis was conducted to examine the thermodynamic mechanisms governing staged latent heat activation and spatial phase-transition evolution within hybrid-melting-point PCM systems.

5.1. Configuration of Composite PCM Blocks

As illustrated in Figure 12, a 10 mm × 10 mm computational domain was defined to evaluate isolated PCM behavior. Two composite configurations with an identical total latent heat capacity (180 J/g) were established to isolate the variable of melting-point distribution. The first configuration, denoted as PCM27–27, serves as a single-transition baseline representing a homogeneous system with a uniform melting temperature of 27 °C. The second configuration, denoted as PCM24–30, represents the proposed hybrid-transition strategy and comprises equal volumetric fractions of PCM24 and PCM30. To simultaneously examine the effect of latent heat magnitude independent of the melting-point distribution, a third configuration, PCM24–30 with a doubled latent heat capacity of 360 J/g, was also evaluated. All blocks were initialized at an equilibrium state of 18 °C and subjected to a constant thermal boundary condition of 35 °C on the exterior face. This setup ensures purely transient, inward heating from solid-state conditions to fully liquid equilibrium.

5.2. Transient Temperature Evolution and Latent Heat Effects

Figure 13 presents the transient interior temperature evolution of PCM blocks with different melting-point distributions and latent heat capacities. As the material temperature increases from the 18 °C condition toward the imposed 35 °C boundary temperature, deviations from linear sensible heating emerge as the phase-transition intervals are reached.

For the single-transition PCM27–27 (180 J/g), a distinct temperature plateau is observed near 27 °C, corresponding to concentrated latent heat absorption. Following completion of the phase transition, the temperature increases more rapidly as sensible heating becomes dominant. In contrast, the hybrid PCM24–30 (180 J/g) curve exhibits two distinct deceleration regions corresponding to the sequential melting events at 24 °C and 30 °C. Rather than a single concentrated buffering event, the hybrid system distributes thermal resistance across a broader temperature range through staged phase-transition behavior.

Although both the PCM27–27 (180 J/g) and PCM24–30 (180 J/g) systems exhibit different transient temperature profiles, both configurations reach thermal equilibrium at 35 °C within nearly identical time periods. This behavior indicates that the total latent heat storage capacity primarily governs the cumulative thermal storage potential, whereas melting-point distribution influences the temporal distribution of thermal buffering behavior.

Increasing the latent heat capacity of the PCM24–30 system from 180 J/g to 360 J/g significantly prolongs the time required to reach thermal equilibrium. The PCM24–30 (360 J/g) configuration reaches equilibrium at approximately 52 min, representing a 52.9% delay in peak temperature arrival, compared with approximately 34 min for the 180 J/g systems. This extended thermal response indicates that increasing latent heat capacity enhances thermal inertia and delays peak temperature propagation during transient heating.

5.3. Spatial Temperature Distribution and Phase-Front Dynamics

To further investigate the internal heat-transfer mechanisms responsible for staged thermal buffering, spatial temperature contours were extracted at representative center temperatures of 19 °C, 24 °C, 27 °C, 30 °C, and 34 °C, as detailed in Figure 14.

Figure 14 illustrates the temperature contours within the computational domains of PCM24-30 (180 J/g) and PCM27-27 (180 J/g) under center temperatures of 19 °C, 24 °C, 27 °C, 30 °C, and 34 °C. At 19 °C, shown in Figure 14a,b, both materials remain in their solid phase because the corresponding melting thresholds are not yet reached. The distribution of isothermal lines is vertical and uniform across both systems, reflecting an even penetration of heat from the exterior toward the interior without any phase transformation effects.

When the center temperature rises to 24 °C, as presented in Figure 14c,d, differences between the two materials start to emerge. For PCM27-27, the isotherms remain straight because heat transfer proceeds evenly through the homogeneous medium. In contrast, PCM24-30 displays concave curvature toward the central domain. This distortion occurs because the outer layer, composed of PCM24, begins melting, consuming latent heat, and retarding the temperature rise locally. Meanwhile, the PCM30 region at the core remains below its transition threshold and continues to warm steadily in the solid state. The result is a non-uniform thermal profile distinguished by differing rates of temperature evolution in each domain.

At 27 °C, the PCM24 region has largely completed melting, while the PCM30 component remains below its phase-transition threshold. In contrast, the single-transition PCM27–27 system undergoes simultaneous phase transition throughout the computational domain, resulting in a comparatively uniform thermal response.

As the temperature increases toward 30 °C, the PCM30 component within the hybrid system enters its melting interval and introduces a second stage of latent heat absorption. This sequential activation produces additional thermal buffering and further delays temperature propagation within the PCM block.

Once the temperature reaches approximately 34 °C, both PCM systems become fully liquid and the temperature contours return to nearly uniform distributions, indicating completion of the phase-transition process and dominance of sensible heat transfer.

Overall, the contour evolution shown in Figure 14 demonstrates that hybrid-melting-point PCM systems can distribute latent heat absorption across multiple temperature intervals rather than concentrating thermal buffering within a single transition range. This staged phase-transition behavior is consistent with the transient thermal responses observed in Section 4 and helps explain the improved adaptability of hybrid PCM systems under dynamically varying thermal conditions.

6. Conclusions

This study integrates the thermodynamic feasibility and transient thermal performance of hybrid-melting-point PCMs integrated into multilayer building wall systems through controlled numerical simulations. Wall assemblies incorporating conventional single-transition PCM systems and hybrid PCM configurations were evaluated under dynamically varying thermal loading conditions representing mild, hot, and cold regimes.

The results demonstrated that melting-point distribution significantly influences transient thermal regulation behavior. Under moderate thermal conditions, both single-transition and hybrid PCM systems effectively reduced indoor temperature fluctuations relative to the non-PCM reference wall. However, under elevated and reduced thermal loading conditions, the hybrid PCM configuration exhibited improved thermal adaptability by distributing latent heat activation across multiple temperature intervals.

Compared with RW1 (reference wall without PCM integration), the proposed hybrid PCM wall reduced the maximum indoor temperature by up to 18.5% and increased the minimum indoor temperature by up to 51.9%, while maintaining the same total latent heat capacity as the conventional single-transition PCM configuration (RW2). In addition, the revised ITD indices demonstrated improved overheating mitigation and thermal comfort retention under dynamically varying thermal conditions, with several thermal fragments exhibiting complete avoidance of overheating or overcooling excursions.

Material-level PCM block simulations further revealed that staged phase transitions produce sequential latent heat absorption and release behavior over multiple temperature intervals, thereby extending thermal buffering across broader temperature ranges. Spatial temperature contour analysis demonstrated that melting-point distribution influences localized phase-front evolution and transient thermal resistance within PCM domains. These thermodynamic mechanisms help explain the improved transient thermal regulation observed in the hybrid PCM wall systems.

The findings suggest that hybrid-melting-point PCM systems can improve the operational adaptability of latent thermal energy storage within building envelopes without increasing total latent heat storage capacity. Rather than concentrating thermal buffering within a single temperature interval, staged phase-transition behavior enables more continuous thermal regulation under varying thermal conditions.

It should be noted that the present study employed simplified sinusoidal thermal loading conditions intended for controlled thermodynamic interpretation rather than full annual climatic prediction. The objective of the present work was to isolate the intrinsic transient thermal response of staged phase-transition systems under controlled dynamic loading conditions rather than to provide climate-specific building-energy prediction. In addition, practical considerations associated with PCM encapsulation, manufacturability, phase segregation, long-term cyclic durability, and climate-specific performance were not investigated. Future studies should therefore incorporate experimental validation, realistic weather datasets, long-term cyclic behavior, phase-dependent thermal conductivity characterization, and techno-economic evaluation to further assess the practical implementation potential of hybrid PCM systems in building applications.